To create a SwiftUI application that can make phone calls using the Vonage Client SDK and CallKit, you need to deploy a server to handle creating a Vonage Application, Users, JWT Generation, and webhooks. Then, you adapt an iOS application that uses the Vonage Client SDK to make calls using CallKit. The process involves deploying a server, creating a user and generating a JWT, downloading a starter project, updating the provider manager, implementing the CXProviderDelegate, and updating the call model. With these steps, your app can integrate with the system's phone app, display recent calls, and calculate accurate call duration.